The generator matrix

 1  0  0  1  1  1  0  1  1  2  1  2  1  2  1 X+2  X  1  1  1  X  X X+2  1  2  1  2  1  1  1  1 X+2  1  2  1  X  2 X+2  1  1  0 X+2  1  1  1  1  1  2  1  1  1  1  2  0  X  1  0 X+2  X X+2  X  X  1  1  1  1 X+2  1  1  1  1  1  1  0  1  1  1  1  1  1  1
 0  1  0  0  1  1  1  2  1  1  3  1  2  X X+3  1 X+2  X X+1 X+2  1  2  1 X+2  1  X  1 X+1 X+3  3 X+2 X+2  1  1  2  1 X+2  1  2  3  1  0  3 X+2 X+1  0 X+3  2  2 X+3  0  2  1 X+2  1  2  1  X  1  1  1  1 X+2  3  1  X  1  3 X+1 X+3 X+2  1  3  0  2  0  X X+3 X+2  X  0
 0  0  1 X+1 X+3  0 X+1  X  1  3 X+2  X  3  1  0  2  1  3  3  X X+3  1  1 X+3 X+2  0  2 X+1  X X+2 X+3  1  1 X+1  X  X  1  1 X+3 X+3  3  1  0  3  1  0  0  1 X+3 X+1  1  0  X  1  1 X+3  X  1 X+2  2 X+3  X X+3 X+2 X+3  X X+2  X  1  1  3  1 X+2  1  X X+2 X+2  X  3 X+1  0
 0  0  0  2  0  0  0  2  2  2  0  0  0  2  2  2  2  0  2  0  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  0  0  0  2  2  2  2  0  2  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  0  2  2  0  0  0  2  2  0  0  0  2  0  0  2  0  2  0  0
 0  0  0  0  2  0  2  0  2  2  2  2  0  0  2  2  2  2  0  2  0  2  0  2  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  0  2  0  2  0  0  2  0  0  2  2  2  0  0  2  0  2  2  2  0  2  2  2  0  2  0  2  0  0  0  2  0  2  0  2  2  2  2  2  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  0  2  0  2  2  2  2  0  0  2  2  2  0  2  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  2  0  0  0  2  0  0  0  0  0  2  0  2  2  0  2  0  0  0  2  0

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+84x^74+214x^75+318x^76+296x^77+479x^78+328x^79+425x^80+318x^81+324x^82+204x^83+241x^84+188x^85+176x^86+106x^87+143x^88+66x^89+62x^90+42x^91+21x^92+24x^93+25x^94+2x^95+3x^96+4x^97+2x^98

The gray image is a code over GF(2) with n=324, k=12 and d=148.
This code was found by Heurico 1.16 in 1.16 seconds.